Talte Places (of the Planets 81 , ! and 8 ch, through the whole series , any fraction larger than a half being onter a ote am A smallery fa¢hion being 2 }:. I +he majority of ges, as is mude evident by the table, this process yields correct yesults : e })?ve afk} in thr: ; |um of a th's Hine; with a pluk or minus sign 1ch mroup1 = |uty of the since a differ by roye t1nt) : hnlf a minute For {brse 45A |led by the Hindu table.
- is not t; b! *upoked, however, that |he Hindu kine« were originally
obtained by whe ¥o$ described in the tex "ht 10998 wik, it all probability, suggested by observing the successive differences in the values of the sin:g as already etermined by other tutethods. Nor is it difEcult js(vy what were this: htt]: the (7 inhalted by the limit tion of the talk t. : '। differing from one १nother by B° 45ः and by what we m IM!rat of the rigonometric al methods of the Hindus. The two main principles, | Ritl hich bho greater portion of all the Hindu al«ulations are 1 R, re m the one hand, thhe equality of the square of the hypotheruse in | r: ht-lungled triangle to the sum of the squares of the other bro wide* ard, m the other hand, the proportional •e}ation of the u pnt3ttl 1x f siti. 'The first of these principles gave the Hindu, the side of the tmplement of any are of which the fine as already known is being equinl to the squage root of the lif। the between 1he square # reliu { # the सle x]] ' !ed further to he rule for inding e v®xed sine, which is given above in the text : it was plainly e 12al to the (difference between the sine comple. 7men and dinux Again, the companix nily triangles showed that the chord of } a'। y:५५1: proportion between its vensed sine and If |11A |ew । le of half |A1A re of which the $1 !s known it was •qual to half the square root of the prorlturt of the dianretkey to the versed it: {Tlax he Hindus had acute this last rule (oe not directly appa texm the text of this Shant४५, or from the mantary of Ra anaths, which is the one given by or namudaipt and by the published edition: but it is distinctly stated in the connnentary which Davik bud in i hands (e. Res (i. 24}} bpt: | 1 tnfidently askmru a |N •pY 1e evileme= the x.ble is Af ; ior the principles and rulicy which we have here stated would give a table just such * the me here (yongructed. The sime of 90° was obviously equal to आnd the side of 80° to half radius: from he irst would be found th। भjn’ of 45 22° 3) anti 11° 15 from the latte, those of 1. 8), and 3 45'. The kings thus obtained Could giv those of the :Inputatuentury I':, or of 88° 15, 82° 3', 78° 45, 7; :t and to sir bi T ugan would giv those of R7° 30' aul8 = fining he° $I!। he। le of kinew would stom be made uplete for the ewenty-four divisions of the quadvant; but these MOcesses :)\!lk। nothing fythmr. १५ v n1roteinng fractions of 1ninutes which was undesirable, because the syrnety of the +a!ble would
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